The wave finite element method (WFE) for the vibration of waveguides and periodic structures base... more The wave finite element method (WFE) for the vibration of waveguides and periodic structures bases on the decomposition of vectors of degree of freedom (DOF) into left and right waves. This technique permits to reduce all DOF inside the periodic structure. However, this method cannot be applied easily if the periodic structure is subjected to complex or density loads. This article presents an extended WFE for any type of loads. Firstly, the dynamic equation is rewritten to separate the vectors of loads and DOF. Then, by using the same wave base as for the free-loaded structure, we can obtain a decomposition of DOF in this base with a new component which corresponds to the loads. Finally, this decomposition is applied to the classical approaches of WFE. For the dynamic stiffness matrix (DSM approach), it is shown that the external loads have no contribution to the global matrix but they lead to an equivalent load in the dynamic equation. Otherwise, the wave analysis (WA approach) is ...
An urban low-height barrier meant to attenuate tramway noise emission for nearby walking pedestri... more An urban low-height barrier meant to attenuate tramway noise emission for nearby walking pedestrians or cyclists is studied. A numerical method coupling the two dimensional BEM and a gradient-based optimization algorithm is proposed to optimize the admittance distribution on the barrier in order to enhance the broadband insertion loss in the shadowing zone. The gradient of the broadband attenuation is calculated e ciently using the adjoint state approach which makes it possible to use a large number of parameters without significant increase of computation time and to consider a barrier of arbitrary shape. A few admittance designs coupling porous layers and micro-perforated resonant panels covering barriers of classical shapes are proposed, all showing an improvement of several dB(A) compared to more simple admittance distributions.
... Laboratoire Analyse des Matériaux et Identification, Unité Mixte ENPC-LCPC, Ecole Nationale d... more ... Laboratoire Analyse des Matériaux et Identification, Unité Mixte ENPC-LCPC, Ecole Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Champs sur Marne, 77455 Marne La Vallée Cedex, France email: Hieu.Nguyen@lami.enpc.fr ... tr and . ...
In terms of safety and environment, reduction of the noise generated by tire vibrations on a road... more In terms of safety and environment, reduction of the noise generated by tire vibrations on a road is very significant. In order to study the vibration properties of vehicle tires, various methods have been presented in literature. In most of these methods, the global structure of tires has been modelled as circular ring, orthotropic plate, periodic or full 3-dimensional models. A brief review of the characteristics of these models and comparison of their dynamic behaviour are the main purpose of the current study. The tire is supposed to be subjected to an excitation caused by contact of the tire and road. Study of vibrational responses demonstrates that the validity of each model is limited to a certain frequency range. To employ the circular ring and orthotropic plate models, first, we require to estimate some structural and material data associated to the nature of these models. To this end, the vibrational response of a 3D model is considered to determine some properties such as...
The identification of the most dangerous combinations of excitations that a non-linear mechanical... more The identification of the most dangerous combinations of excitations that a non-linear mechanical system can be confronted to is not an easy task. Indeed, in such cases, the link between the maximal values of the inputs and of the outputs is not direct, as the system can be more sensitive to a problematic succession of excitations of low amplitudes than to high amplitudes for each kind of excitations. This work presents therefore an innovative method to identify the combined shapes of excitations that are the most correlated to problematic responses of the studied mechanical system.
Periodically supported beams subjected to a moving load are often used for modelling the railway ... more Periodically supported beams subjected to a moving load are often used for modelling the railway dynamics and analytical solutions have been developed for such modelling [3, 4]. More complex models can be constructed by including supports with damping or non-linear stiffness elements. This study deals with the dynamical modelling of non-ballasted railways, especially railways in tunnels. The model is developed as a dynamical system of multi-degree of freedom. Under the periodic assumption on the reaction force of the supports, the equation of motion for a periodically supported beam subjected to a moving load has been written. Then the Fourier transform has been used to solve this equation in case of damped supports. Analytical solutions have been established for the motion of the wheel and rail and also for the reaction force of the supports. The analytical solutions have been compared with in situ experimental measurements. The comparison shows that the theoretical results agree w...
Abstract—This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-conta... more Abstract—This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.
Many trains have braking systems made of discs and pads which can generate very high noise levels... more Many trains have braking systems made of discs and pads which can generate very high noise levels. During the braking, instabilities can be generated in the contact zone between the pads and the disc, leading to high vibrations and high levels of noise radiations for frequencies typically between 1kHz and 15kHz. Numerical computations of noise radiation at these high frequencies for systems having the size of usual train braking systems and their geometrical complexities are difficult with classical methods and thus require special attention. In this paper, different strategies based on the boundary element methods and approximate methods are used for computing the sound radiation from the knowledge of the surface velocity. Contributions of parts of the system such as the disc, the pads and the caliper to the global sound levels are identified. Analysis of the system radiation in terms of spectra and directivities are also presented.
This paper proposes a multi-domain boundary element method to compute the sound field around bodi... more This paper proposes a multi-domain boundary element method to compute the sound field around bodies with macro porosities. It saves computational cost and is especially suitable for complex structures. It is based on the boundary element method, and divides the computation into an exterior subdomain and several interior subdomains. The subdomains are connected by transfer matrices. This method is applied to study some simple examples for which analytical or BEM results are available. Good agreements between these known solutions and the results of multi-domain BEM can check the accuracy. Then a complicated network with flange is calculated with multi-domain BEM to show the influence of network on sound pressure field.
Tire/road contact is the principal source of car noise at speeds greater than 50 km/h. In this co... more Tire/road contact is the principal source of car noise at speeds greater than 50 km/h. In this context, we have developed a new approach for modelling the tire vibrations and the contact with the rigid road surfaces during rolling. For the tire, a periodic model is used to compute Green's functions. The response of the tire can thus be modelled over a large frequency range. Then a fast convolution and contact model is developed and examples of computations of contact forces are given for real road textures. Spectra of forces for different tire velocities are also computed.
The main goals of the Texture & Noise PREDICT project are to define and implement measurement pro... more The main goals of the Texture & Noise PREDICT project are to define and implement measurement procedures and data processing appropriate to the evaluation of the physical relations between the road characteristics (texture profile, acoustic absorption, mechanical stiffness) and the tire acoustic emission in the medium and low frequency domain. The first phase presented here concerns the development of numerical and analytical models relating to the tire road contact (envelopment) and (radiation (horn effect) processes and the specification of measurement procedures.
It has long been recognized that surface topographies can have crucial influences on damage sever... more It has long been recognized that surface topographies can have crucial influences on damage severity and its spatial distribution during strong earthquakes. Site response analysis of topographical structures could only be solved accurately, economically and under realistic conditions, with the aid of numerical methods such as the Boundary Element Method (BEM). The basic idea of BEM consists of transformation of partial differential equation into a boundary integral equation and obtaining the fundamental solutions of the corresponding adjoint partial differential equations. Then a system of algebraic equations can be formed by bringing the field point to the surface, discretizing of surface and integrating numerically over it. In this paper, three-dimensional fundamental kernels for the integral equations or fundamental solutions of point force and source are obtained in frequency domain, for the dynamic unsaturated poroelasticity governing differential equations which are establishe...
This paper aims at obtaining a 3D fundamental solution for unsaturated soils under dynamic loadin... more This paper aims at obtaining a 3D fundamental solution for unsaturated soils under dynamic loadings in Laplace transform domain using the method of Hormander. These solutions can be used, afterwards, in a convolution quadrature method (CQM)-based boundary element formulations in order to model the wave propagation phenomena in such media in time domain.
Traffic noise is considered by people as one of the most important sources of environmental disco... more Traffic noise is considered by people as one of the most important sources of environmental discomfort. A way to limit the traffic noise is to reduce the noise emission, for example, by using specific low noise pavements, particularly in suburban areas. However, in real situations, it can be difficult to evaluate the impact of a given pavement, because it depends, for example, on the road geometry, the meteorological conditions, or the distance of the receiver position. Finally it can be difficult to select the most appropriate pavement for a given noise reduction objective. In this paper, a simple method is proposed to evaluate the noise impact of a pavement, in typical road geometries and environmental conditions. The proposed approach uses two databases, the first one based on measurements of emission spectra of road vehicles on several typical pavements, the second one made of pre-calculations of noise propagation for typical road configurations. Finally, the method is implement...
The wave finite element method (WFE) for the vibration of waveguides and periodic structures base... more The wave finite element method (WFE) for the vibration of waveguides and periodic structures bases on the decomposition of vectors of degree of freedom (DOF) into left and right waves. This technique permits to reduce all DOF inside the periodic structure. However, this method cannot be applied easily if the periodic structure is subjected to complex or density loads. This article presents an extended WFE for any type of loads. Firstly, the dynamic equation is rewritten to separate the vectors of loads and DOF. Then, by using the same wave base as for the free-loaded structure, we can obtain a decomposition of DOF in this base with a new component which corresponds to the loads. Finally, this decomposition is applied to the classical approaches of WFE. For the dynamic stiffness matrix (DSM approach), it is shown that the external loads have no contribution to the global matrix but they lead to an equivalent load in the dynamic equation. Otherwise, the wave analysis (WA approach) is ...
An urban low-height barrier meant to attenuate tramway noise emission for nearby walking pedestri... more An urban low-height barrier meant to attenuate tramway noise emission for nearby walking pedestrians or cyclists is studied. A numerical method coupling the two dimensional BEM and a gradient-based optimization algorithm is proposed to optimize the admittance distribution on the barrier in order to enhance the broadband insertion loss in the shadowing zone. The gradient of the broadband attenuation is calculated e ciently using the adjoint state approach which makes it possible to use a large number of parameters without significant increase of computation time and to consider a barrier of arbitrary shape. A few admittance designs coupling porous layers and micro-perforated resonant panels covering barriers of classical shapes are proposed, all showing an improvement of several dB(A) compared to more simple admittance distributions.
... Laboratoire Analyse des Matériaux et Identification, Unité Mixte ENPC-LCPC, Ecole Nationale d... more ... Laboratoire Analyse des Matériaux et Identification, Unité Mixte ENPC-LCPC, Ecole Nationale des Ponts et Chaussées, 6-8 avenue Blaise Pascal, Champs sur Marne, 77455 Marne La Vallée Cedex, France email: Hieu.Nguyen@lami.enpc.fr ... tr and . ...
In terms of safety and environment, reduction of the noise generated by tire vibrations on a road... more In terms of safety and environment, reduction of the noise generated by tire vibrations on a road is very significant. In order to study the vibration properties of vehicle tires, various methods have been presented in literature. In most of these methods, the global structure of tires has been modelled as circular ring, orthotropic plate, periodic or full 3-dimensional models. A brief review of the characteristics of these models and comparison of their dynamic behaviour are the main purpose of the current study. The tire is supposed to be subjected to an excitation caused by contact of the tire and road. Study of vibrational responses demonstrates that the validity of each model is limited to a certain frequency range. To employ the circular ring and orthotropic plate models, first, we require to estimate some structural and material data associated to the nature of these models. To this end, the vibrational response of a 3D model is considered to determine some properties such as...
The identification of the most dangerous combinations of excitations that a non-linear mechanical... more The identification of the most dangerous combinations of excitations that a non-linear mechanical system can be confronted to is not an easy task. Indeed, in such cases, the link between the maximal values of the inputs and of the outputs is not direct, as the system can be more sensitive to a problematic succession of excitations of low amplitudes than to high amplitudes for each kind of excitations. This work presents therefore an innovative method to identify the combined shapes of excitations that are the most correlated to problematic responses of the studied mechanical system.
Periodically supported beams subjected to a moving load are often used for modelling the railway ... more Periodically supported beams subjected to a moving load are often used for modelling the railway dynamics and analytical solutions have been developed for such modelling [3, 4]. More complex models can be constructed by including supports with damping or non-linear stiffness elements. This study deals with the dynamical modelling of non-ballasted railways, especially railways in tunnels. The model is developed as a dynamical system of multi-degree of freedom. Under the periodic assumption on the reaction force of the supports, the equation of motion for a periodically supported beam subjected to a moving load has been written. Then the Fourier transform has been used to solve this equation in case of damped supports. Analytical solutions have been established for the motion of the wheel and rail and also for the reaction force of the supports. The analytical solutions have been compared with in situ experimental measurements. The comparison shows that the theoretical results agree w...
Abstract—This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-conta... more Abstract—This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.
Many trains have braking systems made of discs and pads which can generate very high noise levels... more Many trains have braking systems made of discs and pads which can generate very high noise levels. During the braking, instabilities can be generated in the contact zone between the pads and the disc, leading to high vibrations and high levels of noise radiations for frequencies typically between 1kHz and 15kHz. Numerical computations of noise radiation at these high frequencies for systems having the size of usual train braking systems and their geometrical complexities are difficult with classical methods and thus require special attention. In this paper, different strategies based on the boundary element methods and approximate methods are used for computing the sound radiation from the knowledge of the surface velocity. Contributions of parts of the system such as the disc, the pads and the caliper to the global sound levels are identified. Analysis of the system radiation in terms of spectra and directivities are also presented.
This paper proposes a multi-domain boundary element method to compute the sound field around bodi... more This paper proposes a multi-domain boundary element method to compute the sound field around bodies with macro porosities. It saves computational cost and is especially suitable for complex structures. It is based on the boundary element method, and divides the computation into an exterior subdomain and several interior subdomains. The subdomains are connected by transfer matrices. This method is applied to study some simple examples for which analytical or BEM results are available. Good agreements between these known solutions and the results of multi-domain BEM can check the accuracy. Then a complicated network with flange is calculated with multi-domain BEM to show the influence of network on sound pressure field.
Tire/road contact is the principal source of car noise at speeds greater than 50 km/h. In this co... more Tire/road contact is the principal source of car noise at speeds greater than 50 km/h. In this context, we have developed a new approach for modelling the tire vibrations and the contact with the rigid road surfaces during rolling. For the tire, a periodic model is used to compute Green's functions. The response of the tire can thus be modelled over a large frequency range. Then a fast convolution and contact model is developed and examples of computations of contact forces are given for real road textures. Spectra of forces for different tire velocities are also computed.
The main goals of the Texture & Noise PREDICT project are to define and implement measurement pro... more The main goals of the Texture & Noise PREDICT project are to define and implement measurement procedures and data processing appropriate to the evaluation of the physical relations between the road characteristics (texture profile, acoustic absorption, mechanical stiffness) and the tire acoustic emission in the medium and low frequency domain. The first phase presented here concerns the development of numerical and analytical models relating to the tire road contact (envelopment) and (radiation (horn effect) processes and the specification of measurement procedures.
It has long been recognized that surface topographies can have crucial influences on damage sever... more It has long been recognized that surface topographies can have crucial influences on damage severity and its spatial distribution during strong earthquakes. Site response analysis of topographical structures could only be solved accurately, economically and under realistic conditions, with the aid of numerical methods such as the Boundary Element Method (BEM). The basic idea of BEM consists of transformation of partial differential equation into a boundary integral equation and obtaining the fundamental solutions of the corresponding adjoint partial differential equations. Then a system of algebraic equations can be formed by bringing the field point to the surface, discretizing of surface and integrating numerically over it. In this paper, three-dimensional fundamental kernels for the integral equations or fundamental solutions of point force and source are obtained in frequency domain, for the dynamic unsaturated poroelasticity governing differential equations which are establishe...
This paper aims at obtaining a 3D fundamental solution for unsaturated soils under dynamic loadin... more This paper aims at obtaining a 3D fundamental solution for unsaturated soils under dynamic loadings in Laplace transform domain using the method of Hormander. These solutions can be used, afterwards, in a convolution quadrature method (CQM)-based boundary element formulations in order to model the wave propagation phenomena in such media in time domain.
Traffic noise is considered by people as one of the most important sources of environmental disco... more Traffic noise is considered by people as one of the most important sources of environmental discomfort. A way to limit the traffic noise is to reduce the noise emission, for example, by using specific low noise pavements, particularly in suburban areas. However, in real situations, it can be difficult to evaluate the impact of a given pavement, because it depends, for example, on the road geometry, the meteorological conditions, or the distance of the receiver position. Finally it can be difficult to select the most appropriate pavement for a given noise reduction objective. In this paper, a simple method is proposed to evaluate the noise impact of a pavement, in typical road geometries and environmental conditions. The proposed approach uses two databases, the first one based on measurements of emission spectra of road vehicles on several typical pavements, the second one made of pre-calculations of noise propagation for typical road configurations. Finally, the method is implement...
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